"Operations" means things like add, subtract, multiply, divide, squaring, etc. If it isn't a number it is probably an operation. But, when you see something like ...7 + (6 × 52 + 3)... what part should you calculate first?
Start at the left and go to the right? Or go from right to left?Warning: Calculate them in the wrong order, and you will get a wrong answer ! So, long ago people agreed to follow rules when doing calculations, and they are:
Order of Operations
Do things in Parentheses First. Example:
yes
6 × (5 + 3)
6 × 8
48
no
6 × (5 + 3)
30 + 3
33
(wrong)
Exponents (Powers, Roots) before Multiply, Divide, Add or Subtract. Example:
yes
5 × 22
5 × 4
20
no
5 × 22
102
100
(wrong)
Multiply or Divide before you Add or Subtract. Example:
yes
2 + 5 × 3
2 + 15
17
no
2 + 5 × 3
7 × 3
21
(wrong)
Otherwise just go left to right. Example:
yes
30 ÷ 5 × 3
6 × 3
18
no
30 ÷ 5 × 3
30 ÷ 15
2
(wrong)
How Do I Remember It All ... ? PEMDAS !
P
Parentheses first
E
Exponents (ie Powers and Square Roots, etc.)
MD
Multiplication and Division (left-to-right)
AS
Addition and Subtraction (left-to-right)
Divide and Multiply rank equally (and go left to right).
Add and Subtract rank equally (and go left to right)
After you have done "P" and "E", just go from left to right doing any "M" or "D" as you find them.
Then go from left to right doing any "A" or "S" as you find them.
You can remember by saying "Please Excuse My Dear Aunt Sally".
Note: in the UK they say BODMAS (Brackets,Orders,Divide,Multiply,Add,Subtract), and in Canada they say BEDMAS (Brackets,Exponents,Divide,Multiply,Add,Subtract). It all means the same thing! It doesn't really matter how you remember it, just so long as you get it right.
Examples
Example: How do you work out 3 + 6 × 2 ? Multiplication before Addition:
First 6 × 2 = 12, then 3 + 12 = 15
Example: How do you work out (3 + 6) × 2 ? Parentheses first:
First (3 + 6) = 9, then 9 × 2 = 18
Example: How do you work out 12 / 6 × 3 / 2 ? Multiplication and Division rank equally, so just go left to right:
First 12 / 6 = 2, then 2 × 3 = 6, then 6 / 2 = 3
Oh, yes, and what about 7 + (6 × 52 + 3) ?
7 + (6 × 52 + 3)
7 + (6 × 25 + 3)
Start inside Parentheses, and then use Exponents First
Pre/Alg 1st Period
1st Quarter Survey
Please answer the questions below.
10/22
Operations
"Operations" means things like add, subtract, multiply, divide, squaring, etc. If it isn't a number it is probably an operation.But, when you see something like ...7 + (6 × 52 + 3)... what part should you calculate first?
Start at the left and go to the right?
Or go from right to left?Warning: Calculate them in the wrong order, and you will get a wrong answer !
So, long ago people agreed to follow rules when doing calculations, and they are:
Order of Operations
Do things in Parentheses First. Example:
Exponents (Powers, Roots) before Multiply, Divide, Add or Subtract. Example:
Multiply or Divide before you Add or Subtract. Example:
Otherwise just go left to right. Example:
How Do I Remember It All ... ? PEMDAS !
Divide and Multiply rank equally (and go left to right).
Add and Subtract rank equally (and go left to right)
Then go from left to right doing any "A" or "S" as you find them.
Examples
Example: How do you work out 3 + 6 × 2 ?
Multiplication before Addition:
First 6 × 2 = 12, then 3 + 12 = 15
Example: How do you work out (3 + 6) × 2 ?
Parentheses first:
First (3 + 6) = 9, then 9 × 2 = 18
Example: How do you work out 12 / 6 × 3 / 2 ?
Multiplication and Division rank equally, so just go left to right:
First 12 / 6 = 2, then 2 × 3 = 6, then 6 / 2 = 3
Oh, yes, and what about 7 + (6 × 52 + 3) ?
Do questions 1-10
Worksheet #4a
Watch Video at home and take notes in a google doc. Please share with me your notes. Be prepared to do similar problems in class.
10/24
Work Sheet #4
10/26
Place Value Game
Please show me a when you complete the game.